Problem: The Green Goober, a wildly unpopular superhero, mixes $3$ liters of yellow paint with $5$ liters of blue paint to make $8$ liters of special green paint for his costume. Write an equation that relates $y$, the amount of yellow paint in liters, and $b$, the amount of blue paint in liters, needed to make the Green Goober's special green paint.
Solution: Let's find the constant of proportionality. In the proportional relationship between $y$, the amount of yellow paint in liters, and $b$, the amount of blue paint in liters, one constant of proportionality is the ratio of yellow to blue paint. It is the number we multiply by the amount of blue paint to get the amount of yellow paint. $b\,\times\, ?=y$ $\begin{aligned} b\,\times\, {?}&=y \\\\ {?}&=\dfrac{y}{b} \\\\ &=\dfrac{3}{5} \\\\ &={0.6} \end{aligned}$ The constant of proportionality is ${0.6}$. This means we can multiply ${0.6}$ by the amount of blue paint to get the amount of yellow paint. Now, let's write the equation: $\begin{aligned} \text{amount of yellow paint}&={\text{yellow to blue ratio}}\times\text{amount of blue paint} \\\\ y&={0.6}b \end{aligned}$ One correct equation is: $y = 0.6b$